The true genius of Pants1000's neglected insight is not only that it helps us see that it's ok to mix boosts and degrades, but that it gives us the framework for figuring out true equivalence.
But, "Hark!" I hear you cry, "What exactly is this 'equivalence' of which you equivocate?" -- I'm glad you asked. What I mean by "equivalence" is a process or conception that would allow one to compare, for example, the relative merits of a +100 increase in base stats with, say, the value of loosing a combo that gives 6% team boost instead of 5% or a host of factors such as:
- Base stats
- Combo usage
- Combo effect
- Ability usage (sometimes called PROC, but see my collected works)
- Ability effect
- and actually, I think that's the whole list, but still! -- hmmm, maybe overboosting should be on here...
Equivalence is a processes whereby each of these factors (currently operating in different base units -- apples and oranges as the analogy goes) are standardized into a compatible unit (say fruit) so they can be (...wait for it) fruitfully compared ;)
Let's do some easy examples and then, if we're all feeling comfortable, go full monty:
One might have an ally mate (ign: Maria4evas or HeadOverHills) ask, "What's the better combo, Elite Agents or Cold Hearts?" Blather blather blather is probably the usual discussion, but lets turn to MATH (again, first the simplified example).
IN this simplified example, EVERY CARD IN THE GAME HAS THE SAME BASE STATS. They all happen to be 100 (ATK and DEF). {Note: this is brought to you by the same folks who brought you frictionless surfaces in your physics problems -- GO THEORY!} -- SO both combos require 3 cards -- in a typical 5 card deck, you have two additional cards (also magically same stats!) for a base ATK of 500 {still with me, right?} For this simplified exercise, we're going to ignore everything BUT combos.
Elite Agents boosts all the heroes 6%, so each card gets 6 extra ATK points (100*6% x 5) or a total bonus of 30 and total ATK of 530.
Cold Hearts only boosts 3 cards, but it boosts them 10%, so (100*10% x3) or a total bonus of 30 and a total ATK of 530.
BUT WAIT, there's more.
In survival mode, you only have a 3 card deck, so Elite agents EQUIVALENCE bonus is only 18 while Cold Hearts is still 30 (total hypothetical attacks 318 < 330). As Pants said, it will give you a better "win factor"
A 7% bonus combo will give you a 35 Equivalence on a 5 card deck but only a 21 on a survival -- so it beats the 30 in some cases if you can build flexibility into your decks for different situations. And of course people have already worked out degrade equivalences [add link here if I don't get too lazy].
But this is fairly basic stuff, right? LET'S GET DANGEROUS
Suprise! All cards aren't actually 100 ATK/DEF and there are abilities we need to consider too. So lets get down to business*...
Typically standardization is done to a 100 point scale. {Speaking as a psychologist, this is why, definitionally, average IQ is always 100 -- that's just what it means}. So we're actually going to perpetuate our concept of a 100 point base card, but now we're going to realize that those are standard points-the sort of scalable thing that you'd use in setting a curve. At every rarity, there is a sort of "balancing point" where cards that are stronger on offense get weaker on defense and vice-versa on a type of proportion and then there's the exact even point like Stamford Survivor Speedball -- I'm going to suggest that as the "100%" point and cards with better ATK/DEF be assigned an equivalence score (ES?) as a proportion of that. So a Guns Blazing Rocket Raccoon would have an ES (let's go with it for now) of 100.615 ATk and 99.365 DEF. Secret Avenger Sharon Carter gets ES's of 105.029 ATK and 94.961 DEF. *cough cough*gamebalance*cough* (this was at the fused PMM level--base ratios didn't average to 100 as neatly after the decimal places, but I'm sure savvy observers have some explanations on that front).
> Incidentally, as I'm alluding to, this method can be used to ascertain which cards are disproportionally endowed with massive tracts of stats (i.e. when ATK and DEF ES average out to over 100 -- you know what cards I'm talking about).
So, we've turned stats from numbers into ratios (%'s) but is it enough? Are they commensurate with our other factors? Combo boosts and ability boosts are already frankly commensurate, if you take into account factors such as those I discussed in the simple case scenario above {at this point, a discussion of the weighting of USAGE cases will probably have to wait until a "part 2" since this blog is getting long for me, I can only imagine what it's doing for you} -- that is to say, a 6% hero boost from a combo can already be directly compared to a 10% boost to tactics, etc. But what we're really after is the equivalence that will allow us to understand how much of an increase/decrease in stats is worth an extra X% boost (and, apparently in part 2, at what odds of occurrence?)
Well, now we've come full circle. I can't do better than reference Pant's formula which is basically a ratio of the first half of the alphabet over the latter ;)
If I could permit some liberties:
ESF (Equivalence Score Factor?) would look something like: (C1+C2+C3...)*B1*B2*B3*ComboBoost [you may also factor in alliance position and occasionally scrapper, if you will, but that's more for the ratio version, this is the isolated deck version] where C1-5 are the cards B1-3 are the boost/degrades listed as boost equivalence (remember, that's the focus here) and ComboBoost shouldn't need to be explained. The Adaptor bonus (1.07) will factor out in ratios against an enemy and can be eliminated. Pants's WF (Win Factor) is (more or less) the ratio of your deck's ESF to your opponents -- for simplicity's sake, I'm suggesting that your degrades be treated as boost equivalents, because in a ratio, they are. [Again, USAGE is another matter and the subject of most of my other posts].
So if ESF=(C1+C2+C3)*B1*B2*B3*ComboBoost {survival configuration} then a 10% increase in a single card could be similar to a 3 point something % boost and if {standard configuration} ESF=(C1+C2+C3+C4+C5)*B1*B2*B3*ComboBoost then 10% more on a card might be roughly equivalent to 2% more on a combo or other boost (if it were an affect all sort of thing, for others configurations, I trust you can do your own math).
Hopefully, this is enough to be going on with
- I got you singing, didn't I? Mindworm!